If you look at the Lanz/Odermatt equation, you will see penetration depth in the hypervelocity domain is much much more than a matter of energy. In it, penetration is proportional to (among other factors) the square of the ratio of penetrator and target densities, and the penetrator density times the square of velocity (as opposed to energy, being mass times the square of velocity).

Steel is much less dense than DU/Ti or WHA -- 7.86 g/cc compared to 18.8 g/cc and 17.0 g/cc, respectively. This puts a stiff penalty on steel's performance as a hypervelocity penetrator.

That is curious. I thought the entire advantage of DU was that it sharpened at high velocity where as tungsten flattened? I assume the problem is cross sectional? IE, the long rod snaps under the load?

That is curious. I thought the entire advantage of DU was that it sharpened at high velocity where as tungsten flattened? I assume the problem is cross sectional? IE, the long rod snaps under the load?

The standard equations cannot handle fracturing, it is far too hard to model in such an elegant manner. Maybe this is from experimental data ?

Because the graphics shows penetration at a constant 10 MJ energy and a constant L/D ratio of 30. Meaning: on the left side of the graph, the penetrator is heavier (and due to the fact that the L/D ratio is fixed, it also is longer & thicker), while on the right side of the graph the penetrator will be smaller (shorter & thinner). This image only shows the optimal velocity for L/D 30:1 penetrator with 10 MJ energy, not the relation of penetration and velocity of a constant penetrator shape.

Because the graphics shows penetration at a constant 10 MJ energy and a constant L/D ratio of 30. Meaning: on the left side of the graph, the penetrator is heavier (and due to the fact that the L/D ratio is fixed, it also is longer & thicker), while on the right side of the graph the penetrator will be smaller (shorter & thinner). This image only shows the optimal velocity for L/D 30:1 penetrator with 10 MJ energy, not the relation of penetration and velocity of a constant penetrator shape.

Yes I understood that, I suppose the question really is 'why is the optimum velocity for DU lower than for Tungsten and especially steel'. I can understand the effect for steel as the lower density means the rod is physically bigger for the same velocity and energy, so there is more to be gained from higher velocity and correspondingly smaller projectile.

DU is denser and therefore heavier. That means at the same velocity in the graph, the DU rod will be shorter. That is one of the key factors why it seems that the optimum velocity for DU would be lower; at higher velocities (and a fixed 10 MJ), the DU rod becomes too short for optimal penetration.

This is also one of the reasons why the overall penetration of tungsten is displayed as being higher in the graph: the longer tungsten rod can get closer to optimum velocities.

DU is denser and therefore heavier. That means at the same velocity in the graph, the DU rod will be shorter. That is one of the key factors why it seems that the optimum velocity for DU would be lower; at higher velocities (and a fixed 10 MJ), the DU rod becomes too short for optimal penetration.

This is also one of the reasons why the overall penetration of tungsten is displayed as being higher in the graph: the longer tungsten rod can get closer to optimum velocities.

It's a very interesting question, and it appears to have little to do with energy. I played around with Willi Odermatt's penetration calculator on his website (http://www.longrods.ch/equation.php), and it doesn't seem to have anything to do with length.

Comparing a DU rod (18000 kg/m^3) and WHA rod (17000 kg/m^3) with identical dimensions and identical striking velocity of 1800 m/s, the WHA rod penetrates a few cm more, even though the DU rod has higher bulk density and higher energy. This is for a 300 BHN target with a density of 7850 kg/m^3 at 60 degrees obliquity. Comparing the same two rods against the same target but at a striking velocity of 1600 m/s, the DU rod penetrates a few cm more.

However, this changes when the obliquity changes. Comparing the DU rod (18000 kg/m^3) and WHA rod (17000 kg/m^3) with identical dimensions and identical striking velocity of 1800 m/s on the same target but at 0 degrees obliquity, the penetration is exactly the same (difference is a hundredth of a percent). For the same 0 degree target but at 1600 m/s, the DU rod penetrates a few cm more than the WHA rod.

So it seems that WHA rods only penetrate more than DU rods on high obliquity targets and at high velocity. Otherwise, DU is better or on par with WHA. Based on this, I guess that WHA handles lateral stress better than DU, allowing it to penetrate more steel at higher obliquity without fracturing during penetration.